This paper is concerned with the asymptotic stability of neutral delay differential systems of the form \[ x'(t)= A x(t) + \sum_{i=1}^m B_i x(t- h_i) + \sum_{i=1}^m C_i x'(t - h_i), \] where \( x(t)\) is the state vector, \( A, B_i, C_i \) are constant matrices and \( h_i\) are constant bounded delays. Further, \(A\) is assumed to be a Hurwitz matrix.
In this context, the author proves a theorem which provides a delay-dependent sufficient condition for the asymptotic stability. Since this sufficient condition depends on the existence of suitable constant matrices \( P, Q_i, X_i, Y_i, Z_i \) such that a big matrix \( \Sigma = \Sigma ( P, Q_i, X_i, Y_i, Z_i)\) depending on these matrices is negative definite, the proposed sufficient condition seems to be appropriate for checking the stability of low dimensional problems as shown for a two-dimensional system with two delays. Finally, as remarked by the author, the sufficient stability condition may be weaker than other similar sufficient conditions based on the logarithmic norm of \(A\).